Instability of optical speckle patterns in cold atomic gases ? S.E. Skipetrov CNRS/Grenoble (Part of this work was done in collaboration with Roger Maynard)

Multiple scattering Random medium Detector Incident wave

Multiple scattering Random medium Detector Incident wave

Multiple scattering Random medium Detector Incident wave L l

Multiple scattering in nonlinear media Disorder Nonlinear part of the dielectric constant Main message of this talk: This intensity is NOT the average intensity ! This is speckle !

Instability of speckle pattern : Intuitive arguments

Weak nonlinearity: Self-phase modulation … in a homogeneous medium Nonlinear medium Laser beam Intensity L Deterministic nonlinear phase shift:

Weak nonlinearity: Self-phase modulation … in a disordered medium Nonlinear medium Laser beam Intensity L Random nonlinear phase shift : Path length l

Fluctuations of nonlinear phase shift Average nonlinear phase shift : Fluctuation of the nonlinear phase shift :

Fluctuations of nonlinear phase shift

Instability of speckle pattern We define a bifurcation parameter For the multiple scattering speckle pattern should become extremely sensitive to any perturbations and finally UNSTABLE where

Instability of speckle pattern : Diagrammatic calculation

Scattered field One has to sum contributions of all wave paths :

Scattered intensity One has to sum contributions of all pairs of wave paths :

Short-range correlation of intensity fluctuations

Long-range correlation of intensity fluctuations Langevin equation : Correlation of Langevin currents : Random Langevin currents :

If disorder is modified … If is modified by, will be modified by

Dynamic equation for Random response function with correlation given by

Instability of speckle pattern : Linear stability analysis

Frequency of oscillation Lyapunov exponent Bifurcation parameter Instability region

Expected manifestation of instability in experiment Time correlation of scattered field Dashed lines: Linear medium Solid lines: Nonlinear medium

Instability of speckle pattern : Cloud of two-level atoms

Two-level atom a b Detuning factor : Life time of the upper level : Transition linewidth : Saturation parameter : Saturation intensity :

“Cloud” of two-level atoms Number of atoms per wavelength 3 : Mean free path at resonance and for : Value of for and :

Scattering and nonlinearity in a cloud of atoms

Bifurcation parameter Realistic parameters [Labeyrie et al. PRA 67, (2003)], Rb 85 : and Instability threshold

Bifurcation parameter Realistic parameters [Labeyrie et al. PRA 67, (2003)], Rb 85 : Instability threshold density  2

Bifurcation parameter maximized over  Realistic parameters [Labeyrie et al. PRA 67, (2003)], Rb 85 : Instability threshold density  2 saturation parameter

Bifurcation diagram Realistic parameters [Labeyrie et al. PRA 67, (2003)], Rb 85 : saturation parameter Instability region

Obvious experimental difficulties Instability can be masked by thermal motion of atoms ► Temperature of the atomic cloud should be lowered Speckle dynamics beyond the threshold is not known with certainty ► One should ensure the absence of other possible sources of decorrelation At too large intensities atoms will be accelerated by the incident beam ► Instability threshold should be reached by increasing the size L of the atomic cloud and not only the laser intensity

Conclusions Nonlinear response of a disordered medium can render the multiple-scattering speckle pattern unstable at arbitrarily low laser intensities, provided the sample size is large enough Cold atomic gases are possible candidates for observa- tion of the instability phenomenon Full description of interaction of (powerful) laser light with atomic gases requires self-consistent treatment accounting for “scattering” of atoms on light potential

FIN